Solve the problem.
-In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of $$2.4 \times 10 ^ { 4 }$$ miles. The orbit is circular, and one revolution around Earth takes 10.1 days. Assuming the radius of the Earth is 3960
Miles, find the linear speed of the satellite. Express the answer in miles per hour to the nearest whole mile.
A) 115 mph
B) 725 mph
C) 15,322 mph
D) 622 mph

Question

Quizplus · Accepted Answer

The linear speed $v$ of the satellite can be found using the formula $v = \frac{2\pi r}{T}$, where $r$ is the radius of the orbit, and $T$ is the period of the orbit in hours. The radius of the orbit is the sum of the Earth's radius and the satellite's altitude above the Earth, which is $3960 + 2.4 \times 10^4 = 2.796 \times 10^4$ miles. The period $T$ is $10.1 \times 24$ hours (since there are 24 hours in a day). Plugging these values into the formula gives:$$v = \frac{2\pi(2.796 \times 10^4)}{10.1 \times 24}$$$$v \approx 725 \, \text{mph}$$Therefore, the linear speed of the satellite is approximately 725 mph, rounded to the nearest whole mile.

Solve the Problem 2.4×1042.4 \times 10 ^ { 4 }2.4×104 Miles the Orbit Is Circular, and One Revolution Around Earth

Solve the Problem $2.4 \times 10 ^ { 4 }$ Miles the Orbit Is Circular, and One Revolution Around Earth